Question

Suppose that the national average for the math portion of the College Board's SAT is 531. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores. If required, round your answers to two decimal places.

(a) What percentage of students have an SAT math score greater than 631?

(b) What percentage of students have an SAT math score greater than 731?

(c) What percentage of students have an SAT math score between 431 and 531?

(d) What is the z-score for student with an SAT math score of 630?

(e) What is the z-score for a student with an SAT math score of 395?

Answer 1

a) 531 + 100 = 631

631 is one standard deviation above the mean.

According to the empirical rule about 68% of the data fall within one standard deviation from the mean.

So 34% of students have an SAT math score greater than 631.

b) 531 + 2 * 100 = 731

731 is two standard deviation above the mean.

According to the empirical rule about 95% of the data fall within two standard deviation from the mean.

So 47.5% of students have an SAT math score greater than 731.

C) 531 - 100 = 431

431 is one standard deviation below the mean.

According to the empirical rule about 68% of the data fall within one standard deviation from the mean.

So 34% of students have an SAT math score between 431 and 531.

d) z-score = (x - )/

= (630 - 531)/100 = 0.99

e) z-score = (x - )/

= (395 - 531)/100 = -1.36